A Fuzzy Simulation-Based Optimization Approach for ...

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2012, Article ID 986867, 13 pagesdoi:10.1155/2012/986867

Research ArticleA Fuzzy Simulation-Based OptimizationApproach for Groundwater Remediation Design atContaminated Aquifers

A. L. Yang,1 G. H. Huang,1 Y. R. Fan,2 and X. D. Zhang3

1 MOE Key Laboratory of Regional Energy Systems Optimization, S&C Academy of Resource andEnvironmental Research, North China Electric Power University, Beijing 102206, China

2 Faculty of Engineering and Applied Science, University of Regina, Regina, SK, Canada S4S 0A23 Bureau of Economic Geology, Jackson School of Geosciences,The University of Texas at Austin, Austin, TX 78713, USA

Correspondence should be addressed to G. H. Huang, [email protected]

Received 22 July 2011; Accepted 17 November 2011

Academic Editor: J. Jiang

Copyright q 2012 A. L. Yang et al. This is an open access article distributed under the CreativeCommons Attribution License, which permits unrestricted use, distribution, and reproduction inany medium, provided the original work is properly cited.

A fuzzy simulation-based optimization approach (FSOA) is developed for identifying optimaldesign of a benzene-contaminated groundwater remediation system under uncertainty. FSOAintegrates remediation processes (i.e., biodegradation and pump-and-treat), fuzzy simulation,and fuzzy-mean-value-based optimization technique into a general management framework. Thisapproach offers the advantages of (1) considering an integrated remediation alternative, (2)handling simulation and optimization problems under uncertainty, and (3) providing a directlinkage between remediation strategies and remediation performance through proxy models. Theresults demonstrate that optimal remediation alternatives can be obtained to mitigate benzeneconcentration to satisfy environmental standards with a minimum system cost.

1. Introduction

Contaminated groundwater due to the spill and leakage of petroleum hydrocarbons maypose significant threats to local environment and human health. This provides an adequatereason for a great effort to remediate such contamination. Previously, many remediationmethods (i.e., pump and treat, bioremediation, surfactant-enhanced aquifer remediation,etc.)were applied to mitigate groundwater contamination. However, many process variablesin a groundwater remediation system, such as well location, pumping rate, oxygen-additionrate, and additive-addition rate, have significant impacts on the performance of remediation

2 Mathematical Problems in Engineering

systems. The deficiency in understanding processes controlling the fate of contaminants maylead to a large inflation of expenses [1]. Simulation and optimization models were thereforedeveloped in order to improve remediation efficiency [2].

Previously, many simulation and optimization methods were undertaken to identifyeffective groundwater remediation strategies [3–5]. Ahmad et al. [6] applied a responsesurface approach to a palm oil mill effluent treatment system for mitigating membranefouling problems. Huang et al. [7] proposed an integrated numerical and physical modelingsystem to tackle natural attenuation and biodegradation processes for site remediation.He et al. [8] provided a coupled simulation-optimization approach for optimal designpumping rates of a pump-and-treat (PAT) system. However, most of previous simulationand optimization methods tended to focus on one fixed remediation technique, leadingto relatively low efficiencies or high costs. For example, bioremediation via anaerobicdechlorination would not be an instantaneous process, which required time to develop theappropriate environmental conditions and to grow a microbial population (i.e., the capabledegradation time may be several months to years) [9]; PATmight require significant costs forcontinuous pumping and extraction, as well as system maintenance; in detail, the operationcost of PAT would be 3 times higher than bioremediation [10]. Therefore, it is essentialto develop simulation and optimization system for integrated remediation alternatives toenhance the remediation efficiency and reduce system cost.

Due to the difficulties in incorporating the complicated numerical simulation modelwithin an optimization framework [11], a series of effective surrogates were applied toreplace complex simulation equations [12–14]. Moreover, uncertainties may extensively existin process forecasting (i.e., measurement and/or estimation errors related to hydrogeologicaland physicochemical parameters), which may significantly increase the complexity relatedto remediation design [15]. In the past decades, many stochastic theories were appliedto optimal groundwater remediation design under uncertainty [16–19]. However, highcomputational cost and amounts of data requirement in stochastic analysis may constrictits application to some practical groundwater remediation problems. Consequently, fuzzyset theory has been used as an supplementary tool for many groundwater remediationoptimization problems [20]. Guan and Aral [21] used fuzzy sets and optimization algorithmsto optimize design of a PAT system under uncertainty. Nasiri et al. [22] developeda decision support system for the prioritization of remediation options based on theestimated compatibility index. The system combined fuzzy sets theory, environmental riskassessment with compatibility analysis procedure, which can be used to find a betterremediation technology. Kerachian et al. [23] proposed a fuzzy game theoretic approach forgroundwater resources management, which combined groundwater simulation models withthe optimization model. Nonetheless, there are few considerations for identifying integratedgroundwater remediation strategies (such as using PAT and bioremediation simultaneously)under uncertainty.

In this paper, a fuzzy simulation-based optimization approach (FSOA) is developedfor identifying optimal remedial strategies for a petroleum-contaminated site. The objectiveentails the following tasks: (i) providing a fuzzy simulation model for biodegradationand PAT remediation processes, (ii) carrying out the model for generating a number ofstatistical samples, (iii) developing a fuzzy-mean-value-based optimization technique, and(iv) applying the proposed method to a petroleum-contaminated site for demonstration.

Mathematical Problems in Engineering 3

Subsurface modeling

Scenarios design and fuzzy simulation

Obtain mean values of fuzzycontaminant concentration

Regression analysis

Integratedsimulation andoptimization

Fuzzy-mean-value-basedoptimization

Optimal control of remediationprocesses

Figure 1: Integrated simulation and optimization framework for remediation-process control.

2. Methodology

FSOA consists of two major components: (2.1) fuzzy simulation and (2.2) fuzzy-mean-value-based optimization. The framework of FSOA is shown in Figure 1. The fuzzy simulationcomponent is used to predict contaminant transport under various remediation scenarios.The obtained contaminant concentrations are presented as fuzzy sets. Then the meanvalues of these fuzzy contaminant concentrations are obtained and applied to establish aset of surrogates for providing a bridge between remediation strategies (pumping ratesat the wells) and contaminant concentrations. Finally a nonlinear optimization method isadvanced by incorporating the surrogates into an optimization framework to identify optimalremediation strategies. The detailed procedures are described in the following sections.

2.1. Stimulation Model

2.1.1. Stimulation of Contaminant Transport Process

In this study, BIOPLUME III is used to simulate organic contaminants transport processesin groundwater, which has been used in many studies [10, 24, 25]. The mass transportequations are solved to calculate the spatial variation of the contaminant concentration [26].In biodegradation processes, the aerobic biodegradation using oxygen as electron acceptorsis simulated as an instantaneous reaction. The general equations are as follows [27]:

∂(bH)∂t

=1Rh

[∂

∂xi

(bDij

∂H

∂xj

)− ∂(bHVi)

∂xi

]− H ′W

n− Q

nδ(x − x(r)

)H,

∂Pb

∂t=

[∂

∂xi

(bDij

∂P

∂xj

)− ∂(bPVi)

∂xi

]− P ′W

n,


ΔHso =P

FO, P = 0 if H >

P

FO,

ΔPos = HFO, H = 0 if P > HFO,

H(x, y, t

)∣∣t=0 = H0

(x, y

),

(x, y

) ∈ Ω, t = 0,

H(x, y, t

)∣∣t=Γ1 = H1

(x, y, t

),

(x, y

) ∈ Γ1, t ≥ 0,

(2.1)

where P is the concentration of oxygen [M/L3]; P ′ is the concentration of oxygen in sourceor sink fluid [M/L3]; Q is the pumping rate [L3/T]; x(r) is the coordinates of the well;ΔHSO is the loss of the contaminant concentration due to aerobic biodegradation; ΔPOS isthe concentration loss of the electron acceptor; FO is the stoichiometric ratio for oxygen; Ω isthe study domain; Γ1 is the first boundary condition.

2.1.2. Fuzzy Simulation

In the past decades, the increasing awareness for uncertainties of porous media led to animproved understanding of contaminant transport in subsurface [14]. Fuzzy set theory iswidely used for addressing uncertainties derived from vagueness in input parameters ofsubsurface models [28, 29]. The primary procedures of fuzzy simulation are as follows [24]:(1) discretize the range of membership grade [0, 1] into a number of α-cut levels; (2) selectan alpha-cut level for fuzzy inputs and generate 2m combinatorial arrays for the input vectorthrough fuzzy vertex analysis, wherem is the number of fuzzy parameters; (3) use the 2m newvectors as inputs for the simulation model and generate 2m outputs; (4) assign the smallestand largest values of outputs to the lower and upper limits, respectively; and (5) return toprocess 2 to assign other α-cut levels and repeat processes 3 and 4. The fuzzy sets of thepredicted items are finally approximated based on the obtained lower and upper boundariesof simulation outputs under various α-cut levels.

2.2. Optimization Model

2.2.1. Fuzzy Regression Analysis

In this subsection, regression analysis is used for studying the relationships between theresponse (y) (i.e., contaminants concentrations) and a number of input variables (xi) (i.e.,pump and injection rates). Considering the uncertainty of the outputs from the simulationmodel, a fuzzy regression analysis method is proposed to build relationships betweencontaminants concentrations and control variables. Then these relationships are used asconstraints in the optimization framework.

Fuzzy regression analysis method consists of four stages, including (i) generatingsolutions through fuzzy simulation model, (ii) obtaining the mean values of the outputs,based on the method proposed by Fortemps and Roubens [30], (iii) fitting the inputs andoutputs through a general polynomial regression analysis, and (iv) testing the predictingperformance of the surrogates. If the surrogates have satisfactory performances, they can beused for substituting the numerical simulation model in further optimization framework.


2.2.2. Fuzzy-Mean-Value-Based Optimization

In a groundwater remediation system, the installation cost can be generally neglectedsince it would be significantly less than well operation cost [31]. In addition, most costsfor a remediation system are mainly functions of well pumping rates. Therefore, in thispaper, the total pumping rate is used as decision variables of the optimization model,which will be minimized subject to environmental and economical constraints in order toobtain a minimum cost for the groundwater remediation system. The constraints of theoptimization model include (i) contaminant concentrations at some locations, which shouldbe less than or equal to a regulated environmental standard; (ii) the injection and extractionrates, which would be limited within a desired range; and (iii) water balance constraint,meaning that the sum of pumping rates at all extraction wells should be equal to the sum ofinjection rates at all injection wells. So, the optimization model can be formulated as follows[8]:

Minimize f = A ×I∑i=1

QIni + B ×

J∑j=1

QExj

subject to Ck

(QIn

i , QExj

)≤ Cmax, k = 1, 2, . . . , K,

I∑i=1

QIni =

J∑j=1

QExj ,

0≤ QIni ≤ QIn

i,max, i = 1, 2, . . . , I,

0≤ QExj ≤ QEx

j,max, j = 1, 2, . . . , J,

(2.2)

where f is the total pumping/extraction cost; A and B are the unit injection and extractioncost, respectively; QIn

i and QExj are the pumping rates for the ith injection well and jth

extraction well, respectively; QIni,max and QEx

j,max are the maximum pumping rates for theith injection well and jth extraction well; Cmax is the maximum acceptable contaminantconcentration; Ck is the expected contaminant concentration of kth monitoring well afterremediation. Ck can be regarded as a polynomial function of injection/extraction rates(Q1, Q2, . . . , Qn). The surrogate can be formulated as follows:

Ck = β0,k +n∑i=1

βi,kQi +n∑i=1

n∑j=1

βij,kQiQj

(i /= j

), (2.3)

where β0,k is an intercept term of surrogate k;∑n

i=1 βi,kQi are linear terms of surrogate k;∑ni=1

∑nj=1 βij,kQiQj (i /= j) are interaction terms of surrogate k; n is the number of explanatory

variables.


Table 1: Parameters of the simulation model.

Input parameter ValuesGrid size 20 × 20Cell size 100 × 100 ftHydraulic conductivity 6.56 × 10−4 ft/secHydraulic gradient 0.005Retardation factor 1.0Anisotropy factor 1.0Background concentration of oxygen 1ppmStorage coefficient 0.2Longitudinal dispersivity Support = (11, 19), Core = 15Transverse dispersivity Support = (1.1, 1.9), Core = 1.5Effective porosity Support = (0.2, 0.4), Core = 0.3

3. Case Study

3.1. Overview of the Study Site

The developed FSOAmodel is applied to a hypothetical petroleum-contaminated aquifer (seeFigure 2). The contaminated plume is assumed to be produced by a leaking undergroundstorage tank (UST). The aquifer system of the site is unconfined, homogeneous, andanisotropy. The stratigraphy consists of sand with the depth varied within 13 and 20 ft fromthe surface. The base of the aquifer ranges in elevation from about −3 to −7 ft, and thegroundwater flow direction is northeastwards with a gradient of approximate 0.005. Thehorizontal hydraulic conductivity across the entire grid is 6.56 × 10−4 ft/sec, and the storagecoefficient is about 0.2. Table 1 shows parts of parameters. The previous UST was at theup gradient location of the site where the benzene concentration (approximate 16mg/L)in groundwater is higher than the regulated environmental guideline (0.005mg/L) [32].Thus, this site may pose impacts on surrounding communities and environment; remediationactions are desired for cleaning up contaminated groundwater.

The integration of PAT and biodegradation for remediating contaminated groundwa-ter can be more efficient and cost-effective in comparison to simple PAT or biodegradation(as stated before). So, 2 injection (biodegradation), 4 (pump and treat) extraction, and3 monitoring wells are constructed to inject nutrients for microorganism, install a PATsystem, and monitor benzene concentrations, respectively. It is suggested that effectivenumber of wells and their behaviors can improve remediation efficiency [33]. A simulation–optimization model is therefore an attractive tool for identifying optimal alternatives onthese design components. However, since fuzzy uncertainty (as stated before) may exist ingroundwater remediation design, fuzzy simulation-based optimization approach (FSOA) isdesired for generating effective solution to address this issue.

3.2. Results Analysis

The simulation model is firstly run m times to generate m samples for further surrogatesconstruction. In this study, 6 explanatory variables (pumping rates of the injection andextraction wells) and 3 response variables (expected contaminant concentrations at themonitoring wells M1 to M3) are interpreted by the surrogates. Within the range of pumping


0

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400

600

800

1000

1200

1400

1600

1800

2000

200 400 600 800 1000 1200 2000180016001400

Bioremediation well Monitoring wellPumping well

B1

B2

M1

M2 M3

P1

P2P3

P4

B1 Well name

X (ft)

Y(f

t)

Figure 2: Simulation domain and well location.

rate between 0.0 and 0.08 ft3/sec, 51 scenarios of operation conditions (b1, b2, p1, p2, p3, andp4) are randomly generated (as listed in Table 2). Since some parameters of the system (e.g.,porosity, dispersivity) are presented as fuzzy sets, a fuzzy simulation model is applied todeal with these uncertain parameters and generate contaminant concentrations under variousoperation scenarios. The outputs of the fuzzy simulation model are also presented as fuzzysets. Therefore, a fuzzy regression method is applied to establish the surrogates betweencontaminant concentrations and operation variables.

Biodegradation injection rates (b1 and b2) in injection wells B1 and B2 and extractionrates (p1, p2, p3, and p4) in extraction wells P1, P2, P3, and P4 are selected as control variablesto produce a series of operation scenarios. The benzene concentrations in monitoring wellsare simulated during a 2-year remediation period under each operation condition. Figure 3shows the results of expected benzene concentrations of wells M1, M2, and M3. It appearsthat different results are generated under different scenarios. Thus, it is worthwhile to identifythe interactive relations between system operation patterns and contaminant concentrations,such that the trade-off between system cost and remediation efficiency can be analyzed.

Figure 4 presents the comparison of the results from fuzzy regression analysis andthe mean value of benzene concentrations from numerical simulation. It is indicated that thefuzzy regression models can generally reflect the variation of benzene concentration underdifferent operation scenarios. The peak values in three monitoring wells can be well caught.The RSME values of three models are 0.03114, 0.102, and 0.0532, respectively. These resultsdemonstrate that the established surrogates have satisfactory prediction accuracy.

A nonlinear optimization model is then developed to identify the optimal operatingconditions. When the maximum concentration standard is set as 0.001mg/L, the injectionrates in wells b1 and b2 are 0.0 and 0.0499 ft3/s, respectively; the extraction rates are


Table 2: Scenarios of flow rates in injection and extraction wells (ft3/sec).

Scenario p1 b1 p2 b2 p3 p41 0.01 0.020 0.01 0.02 0.01 0.0102 0.015 0.030 0.015 0.03 0.015 0.0153 0.012 0.025 0.014 0.025 0.008 0.0164 0.009 0.010 0.021 0.058 0.018 0.0205 0.013 0.037 0.006 0.01 0.02 0.0086 0.02 0.049 0.018 0.036 0.029 0.0187 0.03 0.052 0.025 0.04 0.025 0.0128 0.006 0.044 0.028 0.016 0.021 0.0059 0.025 0.032 0.008 0.033 0.006 0.02610 0.029 0.042 0.017 0.045 0.032 0.00911 0.005 0.029 0.009 0.028 0.012 0.03112 0.007 0.035 0.013 0.038 0.021 0.03213 0.018 0.002 0.012 0.048 0.009 0.01114 0.026 0.057 0.018 0.018 0.011 0.02015 0.016 0.040 0.026 0.022 0.013 0.00716 0.021 0.042 0.019 0.029 0.017 0.01417 0.014 0.026 0.011 0.012 0.005 0.00818 0.019 0.034 0.007 0.019 0.014 0.01319 0.022 0.038 0.02 0.024 0.016 0.00420 0.024 0.008 0.005 0.032 0.007 0.00421 0.005 0.038 0.033 0 0 0.00022 0.033 0.031 0 0.021 0.019 0.00023 0.023 0.087 0.022 0 0.023 0.01924 0 0.008 0.016 0.06 0.035 0.01725 0.008 0.059 0.029 0.006 0.022 0.00626 0.004 0.003 0.021 0.08 0.03 0.02827 0.012 0.029 0.023 0.029 0.013 0.01028 0.02 0.041 0.016 0.031 0.021 0.01529 0.017 0.033 0.006 0.02 0.019 0.01130 0.008 0.026 0.011 0.025 0.011 0.02131 0.011 0.028 0.007 0.015 0.024 0.00132 0.016 0.055 0.021 0.032 0.038 0.01233 0.020 0.074 0.016 0.006 0.012 0.03334 0.029 0.072 0.028 0.060 0.036 0.03935 0.012 0.000 0.022 0.039 0.004 0.00136 0.004 0.024 0.007 0.022 0.003 0.03337 0.018 0.039 0.013 0.026 0.009 0.02538 0.019 0.023 0.005 0.061 0.037 0.02239 0.001 0.016 0.029 0.026 0.003 0.01040 0.027 0.076 0.011 0.005 0.011 0.03341 0.029 0.074 0.001 0.014 0.040 0.01842 0.011 0.072 0.023 0.003 0.008 0.03343 0.010 0.047 0.027 0.040 0.020 0.03044 0.028 0.056 0.009 0.009 0.012 0.01645 0.031 0.057 0.008 0.037 0.027 0.02846 0.022 0.038 0.028 0.078 0.038 0.02847 0.019 0.029 0.004 0.054 0.031 0.03048 0.036 0.080 0.028 0.026 0.027 0.01649 0.018 0.016 0.021 0.058 0.005 0.02950 0.032 0.033 0.025 0.043 0.004 0.01551 0.000 0.014 0.000 0.000 0.000 0.000


0

0.2

0.4

0.6

0.8

1

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49E

xpec

ted

ben

zene

co

ncen

trat

ion

(mg/

L)

Scenario number

C1C2

C3

Figure 3: Expected benzene concentrations under 51 operation scenarios (on day 730).

p1 = 0.027 ft3/s, p2 = 0.0 ft3/s, p3 = 0.0065 ft3/s, and p4 = 0.0164 ft3/s. Under this standard,wells B2 and P1 would play more important role while wells P3 and P4 would have lesscontributions to contaminant reduction. When the maximum concentration standard is set as0.004mg/L, the injection rates are b1 = 0.0 ft3/s and b2 = 0.0492 ft3/s; the extraction ratesare p1 = 0.0267 ft3/s, p2 = 0.0 ft3/s, p3 = 0.0072 ft3/s, and p4 = 0.0153 ft3/s. Comparingresults between these two scenarios, the system is sensitive to variations of the maximumconcentration standard. Under stricter standard, the remediation system should conductlarger pumping rates, which would enhance the remediation efficiency but accordingly causethe growth of remediation cost. Conversely, looser standard would lead to less pumpingrates, which corresponds to low remediation cost and efficiency. Therefore, the developedmethod can help decisionmaker make a trade-off for the operation condition between systemcost and efficiency under uncertainty.

3.3. Discussions

In this study, we consider parameters of soil porosity, longitudinal dispersivity, andtransverse dispersivity as fuzzy sets due to insufficient data for specifying related probabilitydensity functions. Actually, fuzzy simulation can handle more fuzzy parameters. One shouldknow that the uncertainty in output concentration increases as the number of uncertainparameters increases [24]. In addition to the performance of fuzzy simulation, the accuracyof optimization results also depends upon the surrogates used to represent the relationshipsbetween expected concentrations and pumping rates. A major concern is that approximationerrors of surrogates may lead to large deviations of solutions. On one hand, this concerncan be mitigated by using higher-order regression analysis based on large volumes of testingsamples. On the other hand, the approximation accuracy may benefit from improvement ofpretreatment method for uncertain outputs such as fuzzy expected value models [34, 35].

For comparison, if uncertain parameters are defuzzified to generate related repre-sentative deterministic values before conducting simulation, the procedures of defuzzifiedsimulation-based optimization approach (DSOA) can be obtained and generalized as follows:step 1, defuzzify parameters; step 2, generate a number of remediation scenarios; step3, compute the contaminant concentrations under the defuzzified parameters through thesimulator; step 4, establish a set of surrogates for providing bridges between remediationstrategies and contaminant concentrations; step 5, incorporate the surrogates into theoptimization framework; and step 6, solve the optimization model.


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xpec

ted

ben

zene

co

ncen

trat

ion

(mg/

L)

Scenario number

C1

Direct simulation valueRegression analysis value

(a)

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1

1.2

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49

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ecte

d b

enze

ne

conc

entr

atio

n (m

g/L

)

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C2


(b)

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0.24

0.32

0.4

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ecte

d b

enze

ne

conc

entr

atio

n (m

g/L

)

Scenario number

C3


(c)

Figure 4: Regression analysis versus direct simulation in benzene concentrations.

Figure 5 presents mean values of benzene concentration obtained from FSOA versusDSOA at different monitoringwells. Bothmethods used triangular possibility distributions topresent uncertainty. The results from DSOA and FSOA are similar with each other. However,to some extent, DSOA may take an obvious role in reduction of peak value. For example,the mean values of benzene concentrations obtained by DSOA may be 0.254, 0.456, and0.138mg/L at wells M1, M2, andM3, respectively (shown as red remarked). These values arelower than those obtained by FSOA (0.3072, 0.7115, 0.2329). This indicates that DSOA may


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L)

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M1

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FSOA

(a)

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L)

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M2

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FSOA

(b)

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ecte

d b

enze

ne

conc

entr

atio

n (m

g/L

)

Scenario number

M3

DSOA

FSOA

(c)

Figure 5: Simulation results by DSOA versus FSOA in benzene concentrations.

not well represent system uncertainty and may be too idealistic for the effect of remediation.In addition, defuzzification before simulation cannot well reflect the impact of uncertainty tothe simulation model system.

4. Conclusion

In this paper, a fuzzy simulation-based optimization approach (FSOA) has been developedfor supporting process control of remediation at petroleum-contaminated sites. FSOA


integrated fuzzy simulation and fuzzy regression analysis method into a nonlinear op-timization framework for generating desired operation conditions. The developed methodwas applied to a hypothetical petroleum-contaminated case study. FSOA can address theuncertainty of modeling parameters in simulating flow and transport of contaminants ingroundwater and then generate optimal remediation strategies. The results can provide basesfor guiding remediation performances. They are also useful for decision makers to analyzetrade-offs between system cost and treatment efficiency.

Acknowledgments

This paper was supported by the Beijing Municipal Program of Technology Transfer andIndustrial Application, and the Natural Sciences Foundation of China (No. 51190095).

References

[1] Z. Chen, G. H. Huang, and A. Chakma, “Numerical modeling soil and groundwater contamination—a study for petroleum-contaminated site,” Tech. Rep., TransGas-SaskEnergy, Regina, Canada, 1998.

[2] L. He, G. H. Huang, and H. W. Lu, “A stochastic optimization model under modeling uncertaintyand parameter certainty for groundwater remediation design-Part I. Model development,” Journal ofHazardous Materials, vol. 176, no. 1–3, pp. 521–526, 2010.

[3] A. S. Mayer, C. T. Kelley, and C. T. Miller, “Optimal design for problems involving flow and transportphenomena in saturated subsurface systems,” Advances in Water Resources, vol. 25, no. 8–12, pp. 1233–1256, 2002.

[4] D. A. Bau and A. S. Mayer, “Stochastic management of pump-and-treat strategies using surrogatefunctions,” Advances in Water Resources, vol. 29, no. 12, pp. 1901–1917, 2006.

[5] X. S. Qin, “Assessing environmental risks through fuzzy parameterized probabilistic analysis,”Stochastic Environmental Research and Risk Assessment, vol. 26, no. 1, pp. 43–58, 2011.

[6] A. L. Ahmad, S. Ismail, and S. Bhatia, “Optimization of coagulation-flocculation process for palm oilmill effluent using response surface methodology,” Environmental Science and Technology, vol. 39, no.8, pp. 2828–2834, 2005.

[7] Y. F. Huang, G. H. Huang, G. Q. Wang, Q. G. Lin, and A. Chakma, “An integrated numerical andphysical modeling system for an enhanced in situ bioremediation process,” Environmental Pollution,vol. 144, no. 3, pp. 872–885, 2006.

[8] L. He, G. H. Huang, H. W. Lu, and G. M. Zeng, “Optimization of surfactant-enhanced aquiferremediation for a laboratory BTEX system under parameter uncertainty,” Environmental Science andTechnology, vol. 42, no. 6, pp. 2009–2014, 2008.

[9] H. Stroo, H. C. Ward, and B. C. Alleman, In Situ Remediation of Chlorinated Solvent Plumes, SpringerSciences and Business Media, New York, NY, USA, 2010.

[10] H. J. Shieh and R. C. Peralta, “Optimal in situ bioremediation design by hybrid genetic algorithm-simulated annealing,” Journal of Water Resources Planning and Management, vol. 131, no. 1, pp. 67–78,2005.

[11] Y. F. Huang, Development of environmental modeling methodologies for supporting system simulation,optimization and process control in petroleum waste management, Ph.D. thesis, University of Regina,Regina, Canada, 2004.

[12] G. H. Huang, J. B. Li, and I. Maqsood, Numerical Simulation, Risk Assessment, Site Remediation, andMonitoring Design—A Study of Soil and Groundwater Contamination at the Cantuar Field Scrubber SitePrepared for Environmental Affairs, TransGas-SaskEnergy, 2003.

[13] S. Yan and B.Minsker, “Optimal groundwater remediation design using anAdaptiveNeural NetworkGenetic Algorithm,”Water Resources Research, vol. 42, no. 5, Article ID W05407, 14 pages, 2006.

[14] L. He, G. H. Huang, G.M. Zeng, andH.W. Lu, “An integrated simulation, inference, and optimizationmethod for identifying groundwater remediation strategies at petroleum-contaminated aquifers inwestern Canada,” Water Research, vol. 42, no. 10-11, pp. 2629–2639, 2008.

[15] X. S. Qin and Y. Xu, “Analyzing urban water supply through an acceptability-index-based intervalapproach,” Advances in Water Resources, vol. 34, no. 7, pp. 873–886, 2011.


[16] D. A. Bau and A. S. Mayer, “Stochastic management of pump-and-treat strategies using surrogatefunctions,” Advances in Water Resources, vol. 29, no. 12, pp. 1901–1917, 2006.

[17] A. Mantoglou and G. Kourakos, “Optimal groundwater remediation under uncertainty using multi-objective optimization,” Water Resources Management, vol. 21, no. 5, pp. 835–847, 2007.

[18] Y. Xu and X. S. Qin, “Agricultural effluent control under uncertainty: an inexact double-sided fuzzychance-constrained model,” Advances in Water Resources, vol. 33, no. 9, pp. 997–1014, 2010.

[19] S. Yan and B. Minsker, “Applying dynamic surrogate models in noisy genetic algorithms to optimizegroundwater remediation designs,” Journal of Water Resources Planning and Management, vol. 137, no.3, pp. 284–292, 2011.

[20] G.H. Huang andN. B. Chang, “The perspectives of environmental informatics and systems analysis,”Journal of Environmental Informatics, vol. 1, no. 1, pp. 1–7, 2003.

[21] J. Guan and M. M. Aral, “Optimal design of groundwater remediation systems using fuzzy settheory,”Water Resources Research, vol. 40, no. 1, Article ID W01518, 20 pages, 2004.

[22] F. Nasiri, G. Huang, and N. Fuller, “Prioritizing groundwater remediation policies: a fuzzycompatibility analysis decision aid,” Journal of Environmental Management, vol. 82, no. 1, pp. 13–23,2007.

[23] R. Kerachian,M. Fallahnia,M. R. Bazargan-Lari, A.Mansoori, andH. Sedghi, “A fuzzy game theoreticapproach for groundwater resources management: application of Rubinstein Bargaining Theory,”Resources, Conservation and Recycling, vol. 54, no. 10, pp. 673–682, 2010.

[24] R. K. Prasad and S. Mathur, “Health-risk-based remedial alternatives for contaminated aquifermanagement,” Practice Periodical of Hazardous, Toxic, and Radioactive Waste Management, vol. 14, no.1, pp. 61–69, 2010.

[25] M. P. Suarez and H. S. Rifai, “Modeling natural attenuation of total BTEX and benzene plumes withdifferent kinetics,” Ground Water Monitoring and Remediation, vol. 24, no. 3, pp. 53–68, 2004.

[26] H. S. Rifai, C. J. Newell, J. R. Gonzales, S. Dendrou, L. Kennedy, and J.T.Wilson, BIOPLUME III NaturalAttenuation Decision Support System, Version 1.0 User’s Manual, Air Force Center for EnvironmentalExcellence (AFCEE), San Antonio, Tex, USA, 1997.

[27] R. C. Borden and P. B. Bedient, “Transport of dissolved hydrocarbons influenced by oxygen-limitedbiodegradation: 1. Theoretical development,” Water Resources Research, vol. 22, no. 13, pp. 1973–1982,1986.

[28] X. Qin, Y. Xu, and J. Su, “Municipal solid waste-flow allocation planning with trapezoidal-shapedfuzzy parameters,” Environmental Engineering Science, vol. 28, no. 8, pp. 573–584, 2011.

[29] B. D. Xi, X. S. Qin, X. K. Su, Y. H. Jiang, and Z. M. Wei, “Characterizing effects of uncertainties inMSW composting process through a coupled fuzzy vertex and factorial-analysis approach,” WasteManagement, vol. 28, no. 9, pp. 1609–1623, 2008.

[30] P. Fortemps and M. Roubens, “Ranking and defuzzification methods based on area compensation,”Fuzzy Sets and Systems, vol. 82, no. 3, pp. 319–330, 1996.

[31] B. S. Minsker and C. A. Shoemaker, “Dynamic optimal control of in-situ bioremediation of groundwater,” Journal of Water Resources Planning and Management, vol. 124, no. 3, pp. 149–161, 1998.

[32] SERM (Saskatchewan Environment and Resource Management), Risk Based Corrective Actions forPetroleum Contaminated Sites, Province of Saskatchewan, Regina, Canada, 1999.

[33] C. S. Sawyer and M. Kamakoti, “Optimal flow rates and well locations for soil vapor extractiondesign,” Journal of Contaminant Hydrology, vol. 32, no. 1-2, pp. 63–76, 1998.

[34] B. Liu and Y.-K. Liu, “Expected value of fuzzy variable and fuzzy expected value models,” IEEETransactions on Fuzzy Systems, vol. 10, no. 4, pp. 445–450, 2002.

[35] L. G. Shao, X. S. Qin, and Y. Xu, “A conditional value-at-risk based inexact water allocation model,”Water Resources Management, vol. 25, no. 9, pp. 2125–2145, 2011.

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